To achieve a faster convergence rate, we are motivated by the state-of-the-art NIDS [1]} that has a linear convergence rate \(\mathcal {O}(\max \lbrace \frac{L}{\mu },\frac{1}{\rho }\rbrace \log \frac{1}{\epsilon })\)  to find an \(\epsilon \) -optimal solution of original, i.e., \(\Vert \mathbf {x}_i-\mathbf {x}^\star \Vert ^2\le \epsilon ,\forall i\in \mathcal {V}\)  [2]}. NIDS can be written compactly as follows
\(X^{k+1}=\widetilde{W}(2X^k-X^{k-1}-\gamma \nabla F(X^k)+\gamma \nabla F(X^{k-1})),\) 
